Just to be sure, I did a batch change on all Applications to set them as Not Having Rung.  I do not have the Reset Call Timers When A Call Rings This Device set on the Hunt Groups, but it never was set.  I'm not having much luck with the Mitel documentation, and I really don't want to pay a few hundred dollars to our local support to call Mitel and ask.  Nothing against our local support, but they don't have any CSM guys on staff.